Does this list-building software exists?

I notice there are a number of list-building programs floating around. I'm looking for one to work in a specific way, and don't know if this is something that exists....maybe someone can advise me??....

Basically, I want to implement a system that allows people to sign up to start referring people to my list, after they've already been on my list for a while.

Ie: After someone has been on my list for say 2 months, and I have developed a strong relationship with them, is when I want to offer them the opportunity to sign up as an "affiliate" for my list...

...does that make sense?

It seems that the list-building programs that currently exist combine the initial list signup with the signup to be an affiliate for the list. You can't join the list and then signup later to become an affiliate...it is all combined..

The thinking is this:

First of all, after someone has been on my list for a couple of months, they have a relationship with me, and they know the value of the content I deliver through my list, so they will be more likely to want to refer people than someone who just joined.

Second, I have been pitching my products to them for a couple of months, so they are familiar with the value of the products, and what I want to do is offer a promotion where they can get my main product for free by signing up to be an "affilate," and refer X number of people to my list.

Am I making sense here????

This seems pretty straightforward to me, but seems to be a limitation of all the list-building systems I have seen so far..

Does anyone know if there is a program that does this?? Or have any other thoughts on this?

Does it make sense what I am looking for???

Thanks!!
Elliott